1. ## absolute value proof

How do i prove the following using the properties of absolute values?

A) |x|^2 = x^2

B) |x| = sqrt{ x^2}

Thanks

2. Originally Posted by MagicS06
How do i prove the following using the properties of absolute values?

A) |x|^2 = x^2

B) |x| = sqrt{ x^2}

Thanks
For both you can use the fact that:

$|x| = \left \{ \begin{array}{cc}x, &\mbox { if } x \geq 0\\-x, &\mbox { if } x < 0 \end{array}\right.$

and show that the functions on the right satisfy the same function. Part B is actually an alternative definition for |x|